各态历经MIMO互信息：Emre Telatar之后的二十年
Ergodic MIMO Mutual Information: Twenty Years After Emre Telatar
摘要：
在Emre Telatar在1999年的著名工作（迄今为止有14274次引用）中，示出了具有SNR $1/t$的$m\times n$ MIMO瑞利信道矩阵$\mathbf{H}$的互信息\begin{equation*} \mathrm{I} = \ln\det\left( \mathbf{I}_m + \frac{1}{t} \mathbf{HH}^{\dagger} \right) \end{equation*}的期望值可以表示为涉及Laguerre多项式的积分。我们表明，在这项工作中，Telatar的积分表示可以明确评估的形式\begin{equation*} \mathbb{E}\!\left[\mathrm{I}\right]=\sum_{k=0}^{n+m-3}a_{k}t^{k}+\rm e^{t}~\text{Ei}(-t)\sum_{k=0}^{n+m-2}b_{k}t^{k},, \end{equation*}，其中$\text{Ei}(-t)$是指数积分和$a_{k}$，$b_{k}$是已知的常数，不依赖于$t$的有限总和。令人惊讶的是，对这个经典信息论问题的重新兴趣来自量子信息论的最新发展。
英文摘要：
In the celebrated work of Emre Telatar in the year 1999 (14274 citations to date), it was shown that the expected value of the mutual information \begin{equation*} \mathrm{I} = \ln\det\left( \mathbf{I}_m + \frac{1}{t} \mathbf{HH}^{\dagger} \right) \end{equation*} of an $m\times n$ MIMO Rayleigh channel matrix $\mathbf{H}$ with a SNR $1/t$ can be represented as an integral involving Laguerre polynomials. We show, in this work, that Telatar's integral representation can be explicitly evaluated to a finite sum of the form \begin{equation*} \mathbb{E}\!\left[\mathrm{I}\right]=\sum_{k=0}^{n+m-3}a_{k}t^{k}+\rm e^{t}~\text{Ei}(-t)\sum_{k=0}^{n+m-2}b_{k}t^{k},, \end{equation*} where $\text{Ei}(-t)$ is the exponential integral and $a_{k}$, $b_{k}$ are known constants that do not dependent on $t$. The renewed interest in this classical information theory problem came from, quite surprisingly, the recent development in quantum information theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
